Summary
Naturally fractured reservoirs contain a significant amount of the world oil
reserves. A number of these reservoirs contain several billion barrels of oil.
Accurate and efficient reservoir simulation of naturally fractured reservoirs
is one of the most important, challenging, and computationally intensive
problems in reservoir engineering. Parallel reservoir simulators developed for
naturally fractured reservoirs can effectively address the computational
problem.
A new accurate parallel simulator for large-scale naturally fractured
reservoirs, capable of modeling fluid flow in both rock matrix and fractures,
has been developed. The simulator is a parallel, 3D, fully implicit,
equation-of-state compositional model that solves very large, sparse linear
systems arising from discretization of the governing partial differential
equations. A generalized dual-porosity model, the multiple-interacting-continua
(MINC), has been implemented in this simulator. The matrix blocks are
discretized into subgrids in both horizontal and vertical directions to offer a
more accurate transient flow description in matrix blocks. We believe this
implementation has led to a unique and powerful reservoir simulator that can be
used by small and large oil producers to help them in the design and prediction
of complex gas and waterflooding processes on their desktops or a cluster of
computers. Some features of this simulator, such as modeling both gas and water
processes and the ability of 2D matrix subgridding are not available in any
commercial simulator to the best of our knowledge. The code was developed on a
cluster of processors, which has proven to be a very efficient and convenient
resource for developing parallel programs.
The results were successfully verified against analytical solutions and
commercial simulators (ECLIPSE and GEM). Excellent results were achieved for a
variety of reservoir case studies. Applications of this model for several IOR
processes (including gas and water injection) are demonstrated. Results from
using the simulator on a cluster of processors are also presented. Excellent
speedup ratios were obtained.
Introduction
The dual-porosity model is one of the most widely used conceptual models for
simulating naturally fractured reservoirs. In the dual-porosity model, two
types of porosity are present in a rock volume: fracture and matrix. Matrix
blocks are surrounded by fractures and the system is visualized as a set of
stacked volumes, representing matrix blocks separated by fractures (Fig. 1).
There is no communication between matrix blocks in this model, and the fracture
network is continuous. Matrix blocks do communicate with the fractures that
surround them. A mass balance for each of the media yields two continuity
equations that are connected by matrix-fracture transfer functions which
characterize fluid flow between matrix blocks and fractures. The performance of
dual-porosity simulators is largely determined by the accuracy of this transfer
function.
The dual-porosity continuum approach was first proposed by Barenblatt et al.
(1960) for a single-phase system. Later, Warren and Root (1963) used this
approach to develop a pressure-transient analysis method for naturally
fractured reservoirs. Kazemi et al. (1976) extended the Warren and Root method
to multiphase flow using a 2D, two-phase, black-oil formulation. The two
equations were then linked by means of a matrix-fracture transfer function.
Since the publication of Kazemi et al. (1976), the dual-porosity approach has
been widely used in the industry to develop field-scale reservoir simulation
models for naturally fractured reservoir performance (Thomas et al. 1983;
Gilman and Kazemi 1983; Dean and Lo 1988; Beckner et al. 1988; Rossen and Shen
1989).
In simulating a fractured reservoir, we are faced with the fact that matrix
blocks may contain well over 90% of the total oil reserve. The primary problem
of oil recovery from a fractured reservoir is essentially that of extracting
oil from these matrix blocks. Therefore it is crucial to understand the
mechanisms that take place in matrix blocks and to simulate these processes
within their container as accurately as possible. Discretizing the matrix
blocks into subgrids or subdomains is a very good solution to accurately take
into account transient and spatially nonlinear flow behavior in the matrix
blocks. The resulting finite-difference equations are solved along with the
fracture equations to calculate matrix-fracture transfer flow. The way that
matrix blocks are discretized varies in the proposed models, but the objective
is to accurately model pressure and saturation gradients in the matrix blocks
(Saidi 1975; Gilman and Kazemi 1983; Gilman 1986; Pruess and Narasimhan 1985;
Wu and Pruess 1988; Chen et al. 1987; Douglas et al. 1989; Beckner et al. 1991;
Aldejain 1999).
© 2007. Society of Petroleum Engineers
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History
- Original manuscript received:
17 February 2006
- Meeting paper published:
22 April 2006
- Revised manuscript received:
18 January 2007
- Manuscript approved:
18 January 2007
- Version of record:
20 September 2007
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